Bayesian multilevel compositional data analysis: introduction, evaluation, and application

Abstract: Multilevel compositional data are data that are repeatedly measured or clustered within groups and are non-negative and sum to a constant value. These data arise in various settings, such as intensive, longitudinal studies using ecological momentary assessments and wearable devices. Examples include 24h sleep-wake behaviours, sleep architecture, and macronutrients. This article presents a novel method for analysing multilevel compositional data using Bayesian inference. We describe the theoretical details of the data and the models, and outline the steps necessary to implement this method. We introduce the R package multilevelcoda to facilitate the application of this method and illustrate using a real data example. An extensive parameter recovery simulation study verified the robust performance of the method. Across all conditions investigated in the simulation study, the fitted models had minimal convergence issues (convergence rate > 99%) and achieved excellent quality parameter estimates and inference, with an average bias of 0.00 (range -0.09, 0.05) and coverage of 0.95 (range 0.93, 0.97). We conclude the article with recommendations on the use of the Bayesian multilevel compositional data analysis. We hope to promote wider application of this method to gain novel and robust answers to scientific questions.